In Stockton's "The Lady, or the Tiger?" what is unique about the king's arena?

The king's arena in Stockton's "The Lady, or the Tiger?" is not unique because there is a 50% chance that the accused will die an ignominious death. Roman arenas provided such gut-wrenching death scenes as well. The king's arena in this story is unique because the outcome doesn't depend on a criminal's strength or skills in battle. For the person who faces the choice of what is behind two doors, the outcome is determined by chance. The narrator describes the king's justification behind creating such an arena for justice as follows:

This was the king's semibarbaric method of administering justice. Its perfect fairness is obvious. The criminal could not know out of which door would come the lady. . . and the thinking part of the community could bring no charge of unfairness against this plan; for did not the accused person have the whole matter in his own hands?

Based on the information provided from the passage, the unique qualities of this king's arena is that the criminal gets to choose his fate; then, whatever comes out from behind the door is the accused's final reward or punishment.
In Roman arenas, slaves would fight gladiators more than once or until they died. Roman arenas weren't used as courtrooms, either. They were used purely for violent entertainment. As a result of the philosophy behind the arena, the king supplies his subjects and himself with a partially civilized way of dealing with criminals; of course, the civilized part emerges only if criminals choose the lady's door. On the other hand, the arena is also barbaric because of the deaths which occur if criminals choose the door with the tiger behind it. Ultimately, there is hope in the king's arena because there is a choice; and when there is a choice, there is an opportunity for the criminal to escape the punishment of a tiger. The arena is also unique because of the intrigue it provides its audience each time a new criminal is released in it.